• ### I do not understand where the negative in -sqrt x ^ 6 comes from?

4 answers · 8 hours ago
• ### Just a math question I thought of?

Best answer: 　 Three points on the curve y = sinx: A (a, sin a), B (b, sin b), C (c, sin c) where 0 ≤ a < b < c ≤ 2π Triangle ABC has base |AC| = √((a − c)² + (sin a − sin c)²) Line AC has slope = (sin a − sin c) / (a − c) Equation of line AC: y − sin a = (sin a − sin c) / (a − c) (x − a) (a − c) (y − sin a) = (sin a −... show more
Three points on the curve y = sinx:
A (a, sin a), B (b, sin b), C (c, sin c)
where 0 ≤ a < b < c ≤ 2π

Triangle ABC has base |AC| = √((a − c)² + (sin a − sin c)²)

Line AC has slope = (sin a − sin c) / (a − c)
Equation of line AC:
y − sin a = (sin a − sin c) / (a − c) (x − a)
(a − c) (y − sin a) = (sin a − sin c) (x − a)
(sin a − sin c) (x − a) + (c − a) (y − sin a) = 0

Triangle ABC has height = distance from B to line AC
= |(sin a − sin c) (b − a) + (c − a) (sin b − sin a)| / √((sin a − sin c)² + (a − c)²)
= |(b−c) sin a + (c−a) sin b + (a−b) sin c| / √((sin a − sin c)² + (a − c)²)

Area (ABC)
= 1/2 * √((a − c)² + (sin a − sin c)²) * |(b−c) sin a + (c−a) sin b + (a−b) sin c| / √((sin a − sin c)² + (a − c)²)
= 1/2 * |(b−c) sin a + (c−a) sin b + (a−b) sin c|

Using WolframAlpha, we find area is maximized when:

a = 0
b = 1.72545
c = 5.32211
Maximum area = 3.33656

http://www.wolframalpha.com/input/?i=max...

Here is a diagram showing the triangle with maximum area:
https://www.desmos.com/calculator/di4j6s...
You can move the points around on the curve.
The area is shown on the second line.
6 answers · 20 hours ago
• ### Math question help?

x² + 1 = 5
x² + 1 = 5
14 answers · 1 day ago
• ### How do you solve this math question?

John rides his bike one-third of the way from his house to school where he meets his friend, Joe. After he rides another mile John is halfway to school. How far is the school from Joe’s house?
John rides his bike one-third of the way from his house to school where he meets his friend, Joe. After he rides another mile John is halfway to school. How far is the school from Joe’s house?
10 answers · 4 hours ago
• ### If four times certain number,increased by 6 is equal to 94, what is the number?

10 answers · 7 hours ago
• ### Is it cheating to use a math calculator in class when allowed to?

I consider people who use a calculator to add and subtract problems to be too easy and I consider it cheating because I think people should know how to do math by hand. If you are in a Math class when you are allowed to use a calculator, isn’t this cheating? Why would some Math classes allow you to use a calculator... show more
I consider people who use a calculator to add and subtract problems to be too easy and I consider it cheating because I think people should know how to do math by hand. If you are in a Math class when you are allowed to use a calculator, isn’t this cheating? Why would some Math classes allow you to use a calculator but others won’t allow you? Isn’t it cheating in general to do math problems by a calculator because you know you are going to be 100 percent right and not have a challenge to do problems by hand with using scratch paper?
14 answers · 1 day ago
• ### Is 4 5/8 inches the same as 4.6 inches?

I am very confused with fractions. I'm trying to buy an item online and i want to know its dimensions. So is 4 5/8 inches over 4.5 inches?
I am very confused with fractions. I'm trying to buy an item online and i want to know its dimensions. So is 4 5/8 inches over 4.5 inches?
12 answers · 21 hours ago
• ### What is 80,000 a year , monthly ?

11 answers · 1 day ago
• ### How do you simplify?

sec^2(x)/(sec^2(x)-1)
sec^2(x)/(sec^2(x)-1)
10 answers · 1 day ago
• ### Three less than the quotient of a number and 2 equalls 5 use x?

10 answers · 1 day ago
• ### Is it possible to learn all that there is in math?

13 answers · 2 days ago
• ### How many feet in 60 foot diameter circle?

14 answers · 2 days ago
• ### How much is 1/3 from \$4,000?

7 answers · 2 hours ago
• ### The sum of two integers is 12 and the difference of the two integers is 6. What are the integers?

9 answers · 1 day ago
• ### How many 20 dollars bills make 100?

16 answers · 3 days ago
• ### What does cosine actually mean? (as opposed to 'how do you calculate it'!? TIA?

9 answers · 1 day ago
• ### From \$5 to \$8 percent increase?

8 answers · 1 day ago
• ### An Australian runner has recently run 1500 m in 3 min 43 sec. Find his average rate in miles per hour. Round to the nearest mile per hour.?

10 answers · 2 days ago
• ### The sum of a number and 20 divided by 8?

7 answers · 20 hours ago
• ### Probability help?

Ann and Barbara took turns tossing a fair die until one of them tossed a number 6. Ann tossed ﬁrst, Barbara second, Ann third, and so on. Given that Barbara threw the ﬁrst 6, what is the probability that Barbara obtained it on her second toss (that is on the fourth toss overall)?
Ann and Barbara took turns tossing a fair die until one of them tossed a number 6. Ann tossed ﬁrst, Barbara second, Ann third, and so on. Given that Barbara threw the ﬁrst 6, what is the probability that Barbara obtained it on her second toss (that is on the fourth toss overall)?
7 answers · 20 hours ago